In preparing a demonstration on parametrization by arc length for my calculus class, I integrated the function (2+u^2)^(1/2)
from 0 to t, got the appropriate expression, and set it equal to the variable s (for arc length). When I asked DERIVE to solve the resulting expression for t, I got (new expression involving t) = 2 e^(2s). I can't figure out why DERIVE didn't do the last three steps (dividing by 2, taking natural logs, and dividing by 2 again). I had both s and t set as non-negative real variables and had checked the "real" option under SOLVE. The (new expression involving t) is clearly positive, so I can see no mathematical impediment to these operations. Simpler expressions, such as t=2e^(2s) simplify as they should.
Any ideas? I've tried resetting the branch option in "output options" to no avail.
George F. Feissner
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SUNY College at Cortland
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